
where \(\delta =20\)  days is the number of retained time-delays, which can range from 15 to 25 with only minor effects on the results. We have also experimented with richer feature spaces including EOFs of geopotential height, but found these unnecessary. A growing body of theoretical [1]}, [2]} and empirical [3]}, [4]}, [5]}, [6]}, [7]} evidence supports the use of time-delay coordinates as reliable features for related methods.
The \(k\) -means clustering is carried out using scikit-learn [8]} with \(k=M_t\)  on the collection of hindcast trajectories that were running between days \(t\)  and \(t+1\) . The number of clusters is set to \(M_t=170\)  or the number of data points available on day \(t\) , whichever is smaller.
